Level Density in Complex Scaling Method

It is shown that the continuum level density (CLD) at unbound energies can be calculated in the complex scaling method (CSM) where energy spectra of bound states, resonances and continuum states are obtained within L basis functions. In this method, the extended completeness relation is applied to calculation of Green’s functions, and the continuum-state part is approximately expressed by discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss that the scattering phase shifts can be calculated inversely from of the CLD which is well described applying a basis function technique in the CSM.